Intuitionistic Fuzzy Semi HX Ring

IOSR Journal of Mathematics, 2014

In this paper, we define the notion of intuitionistic fuzzy sub HX ring of a HX ring and some of their related properties are investigated. We define the necessity and possibility operators of an intuitionistic fuzzy subset of an intuitionistic fuzzy HX ring and discuss some of its properties. We introduce the concept of an image, pre-image of an intuitionistic fuzzy subset and discuss in detail a series of homomorphic and anti homomorphic properties of an intuitionistic fuzzy set are discussed.

International Journal of Mathematics and Computer Science, 2018

In this paper, we further study the theory of intuitionistic fuzzy rings and give some new concepts such as intuitionistic fuzzy ring with operators, intuitionistic fuzzy ideal with operators , intuitionistic fuzzy quotient ring with operators, etc. while their some elementary properties are discussed.

International Journal of Algebra, 2011

In this paper we present a new formulation of intuitionistic fuzzy rings based on the notion of intuitionistic fuzzy space. A relation between intuitionistic fuzzy ring based on intuitionistic fuzzy space and ordinary rings is obtained in terms of induction and ...

Transstellar Journal , 2019

In this paper, we introduce the concept of-intuitionistic fuzzy ideal and-intuitionistic fuzzy ideal and study their properties.

JTAM (Jurnal Teori dan Aplikasi Matematika)

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.

In this paper a correspondence between the set of all intuitionistic fuzzy ideals of a Γ-semiring and the set of all intuitionistic fuzzy ideals of its operator semirings is established and used them to study some properties of the semiring S_{2}.

Abstract and Applied Analysis, 2013

As we know, intuitionistic fuzzy sets are extensions of the standard fuzzy sets. Now, in this paper, the basic definitions and properties of intuitionistic fuzzy Γ-hyperideals of a Γ-semihyperring are introduced. A few examples are presented. In particular, some characterizations of Artinian and Noetherian Γ-semihyperring are given.

Annals of Pure and Applied Mathematics, 2017

A Q-fuzzy set is a mapping from [0,1] X Q × → where X is the universe of discourse and Q is a non-empty set. Some works has been emanated for this Q-fuzzy set. In all the above work the set 'Q' is treated as a non-empty set without any algebraic structure. This article presents an algebraic structure for Q-fuzzy set over a semiring named as 1 Q-fuzzy set and provide some properties and results.

IJMS, 2012

In this paper, we apply the Yuanli, Zhang, Quanma's idea of intuitionistic anti-fuzzy subgroups to subring and ideal of a ring. We introduce the notion of intuitionistic anti-fuzzy subring and intuitionistic anti-fuzzy ideal of rings, and investigate some related properties.

SSRN, 2021

The main aim of this paper is to investigate the relationship between the characteristic of a ring and the order of an element in the intuitionistic fuzzy environment. We also characterise the term divisor of zero in a ring and study their connection with the ideal of the ring in the intuitionistic fuzzy setting. Some related results are also analyse.